arXiv:2608.02014v2 Announce Type: replace Abstract: Cross-embodiment dexterous grasping aims to synthesize stable grasps across heterogeneous multi-fingered hands with little or no embodiment-specific tuning. Existing interaction-centric methods achieve promising results, but their object representations often underrepresent local surface geometry, hand descriptors do not explicitly capture both morphology and kinematics, and hand-object interaction modeling is typically isotropic. We propose MANGO-Grasp, an anisotropic interaction framework that represents objects as geometry-oriented 3D Gaussian primitives to better preserve local surface geometry, and encodes hands into pretrained descriptors that capture both morphology and kinematics. Hand-object interaction is modeled using anisotropic Mahalanobis fields that reflect the directional nature of contact and guide a shared optimization for grasp realization across embodiments. On the CMAP and MultiGripperGrasp benchmarks, MANGO-Grasp outperforms the strongest seen-hand baseline by up to 8.24 percentage points in simulation. It also transfers zero-shot to the unseen SharpaWave hand, improving over the strongest zero-shot baseline by up to 16.57 percentage points, and achieves 86% success in real-world experiments. The code and additional materials will be made available upon publication at https://connor-zh.github.io/MANGO-Grasp/.